Genotype-phenotype maps and mathy biology

I'm reading a book chapter by Peter Stadler from 2002 called Landscapes and Effective Fitness [1]. It has this absolutely gorgeous figure:

I love it. But just before this figure he has this equation:

I hate it. I hate it because all it says is that each type, x, is at a frequency Px of the total population, so those Px sum to one. But of course. I just don't think this kind of writing is conducive to discourse, because in biology there is already a huge gap between the majority who don't read (and cite) papers with equations, and those who write them. So why muddy the waters with equations like this that says next to nothing?

However, I reiterate (and is why I'm reading the chapter) that this figure of a genotype-phenotype-fitness map is super cool.There are many more different genotypes (the genetic make-up of an organism) than there are different phenotypes (the combined physical attributes of the organism). This must be so, because we now know that each trait is affected by many genes; it takes more than one gene to make a trait (there may be exceptions where only one gene encodes a trait).

The figure is a conceptual map, but real g-p mapping is sort of the holy grail in evolutionary biology at the moment. With a real map like in hand evolutionary dynamics can be predicted, and we will be able to say which genetic changes are required to change the phenotype. However, realistically we can only map a very small portion of the genotype on to the phenotype, and there even seems to be some confusion about what the proper answer is to the question of what the genotype-phenotype map looks like. Hopefully the answer won't be too mathy...

4 comments:

"There are many more different genotypes (the genetic make-up of an organism) than there are different phenotypes (the combined physical attributes of the organism). This must be so, because we now know that each trait is affected by many genes; it takes more than one gene to make a trait (there may be exceptions where only one gene encodes a trait)."

There's a more profound implication there. Many more different genotypes than phenotypes means many genotypes code for the same phenotype. Many solutions to the same problem = robustness.

The set notation is not annoying to read if you've had years of math training. If you see tens of those everyday, reading them becomes second nature, kinda like how regular reading was slow and painful at first (when we were, say, 5), but it was much easier at 10. Is it reasonable for everyone to be fluent in math notation? That's up for debate, but I don't think so. I don't think the author is fluent himself, since the set-builder condition doesn't have proper syntax (for starters, the universal quantifier is in the wrong place).

Pleiotropy comes from the Greek πλείων pleion, meaning "more", and τρέπειν trepein, meaning "to turn, to convert". It designates the occurrence of a single gene affecting multiple traits, and is a hugely important concept in evolutionary biology.

I'm a postdoc at UC Santa Barbara.

All Many aspects of evolution interest me, but my research focus is currently on microbial evolution, adaptive radiation, speciation, fitness landscapes, epistasis, and the influence of genetic architecture on adaptation and speciation.